**IAS/Park City Mathematics Series**

Volume: 8;
2000;
340 pp;
Hardcover

MSC: Primary 22;
Secondary 43; 57

**Print ISBN: 978-0-8218-1941-8
Product Code: PCMS/8**

List Price: $60.00

Individual Member Price: $48.00

# Representation Theory of Lie Groups

Share this page *Edited by *
*Jeffrey Adams; David Vogan*

A co-publication of the AMS and IAS/Park City Mathematics Institute

This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups. The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the year 1975, specifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the Langlands classification.

Additional contributions outline developments in four of the most active areas of research over the past 20 years. The clearly written articles present results to date, as follows: R. Zierau and L. Barchini discuss the construction of representations on Dolbeault cohomology spaces. D. Vogan describes the status of the Kirillov-Kostant “philosophy of coadjoint orbits” for unitary representations. K. Vilonen presents recent advances in the Beilinson-Bernstein theory of “localization”. And Jian-Shu Li covers Howe's theory of “dual reductive pairs”.

Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researchers. Students should have completed the standard introductory graduate courses for full comprehension of the work. The book would also serve well as a supplementary text for a course on introductory infinite-dimensional representation theory.

Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

#### Table of Contents

# Table of Contents

## Representation Theory of Lie Groups

#### Readership

Graduate students and research mathematicians interested in representation theory specifically Lie groups and their representations.

#### Reviews

Altogether, the volume brings a coherent description of an important and beautiful part of representation theory, which certainly will be of substantial use for postgraduate students and mathematicians interested in the area.

-- European Mathematical Society Newsletter